When writing a paper using a method validated by this software, we recommend that you cite the software beyond and provide the raw data used as supplementary material for your paper.
To cite this software :
ValidR - Assay
All statistical were produced using the method described in Hubert, P. et al. 2007. Harmonization of strategies for the validation of quantitative analytical procedures. A SFSTP proposal - part III. J Pharm Biomed Anal 45: 82-96. And algorithm were checked using the data providied with the article.
The \(\beta\) value used for the calculation of the \(\beta\) expectation tolerance interval was set to 0.8 and the acceptance limits was fixed to 5 %.
The estimation of the parameters of the calibration curves was obtained by the ordinary least squares method (OLS) with R version 4.2.2 (2022-10-31) software [@R-base] and the r stats::lm() function was used. .
Response functions \(signal=f(concentration)\) were analyzed using stats4::lm() function in R, using calibration data provided Table 5.1 and Figure 3.1).
Analysis were performed using :
Figure 3.1: Calibration data
The interactive table 3.1 shows the values obtained with regressions :
| Methods | Serie | Intercept | Slope | AIC | R² |
|---|---|---|---|---|---|
| Linear (LM) | 1 | -1372.3658 | 7566912 | 188.82827 | 0.9987755 |
| Linear (LM) | 2 | -2972.4758 | 7166164 | 157.35429 | 0.9999733 |
| Linear (LM) | 3 | -4450.9923 | 7101554 | 178.31360 | 0.9996262 |
| Linear 0 (LM) | 1 | 0.0000 | 7559371 | 186.84949 | 0.9991446 |
| Linear 0 (LM) | 2 | 0.0000 | 7149831 | 159.29751 | 0.9999694 |
| Linear 0 (LM) | 3 | 0.0000 | 7077097 | 177.10514 | 0.9997112 |
| Linear 0-max (LM) | 1 | 0.0000 | 7559800 | 52.44744 | 0.9991522 |
| Linear 0-max (LM) | 2 | 0.0000 | 7151585 | 43.89910 | 0.9999868 |
| Linear 0-max (LM) | 3 | 0.0000 | 7083672 | 48.34795 | 0.9998756 |
| Linear weighed 1/X (LM) | 1 | -1495.9007 | 7569138 | 165.77039 | 0.9987966 |
| Linear weighed 1/X (LM) | 2 | -2165.6005 | 7151626 | 156.85434 | 0.9995574 |
| Linear weighed 1/X (LM) | 3 | -530.7419 | 7030919 | 166.86941 | 0.9984005 |
| Linear weighed 1/Y (LM) | 1 | -1709.6429 | 7563307 | 165.04285 | 0.9986945 |
| Linear weighed 1/Y (LM) | 2 | -2215.1444 | 7146698 | 159.77107 | 0.9991691 |
| Linear weighed 1/Y (LM) | 3 | -575.2321 | 7018751 | 167.75477 | 0.9981079 |
The residues obtained are shown in the interactive figure 3.2.
You can click or double-click on a legend to isolate or display a curve. You can zoom in on a part of the figure.
Figure 3.2: Relative bias calculated from regression
Trueness and precision are depicted on table 4.1 and 4.2
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias NULL | Repeatability SD NULL | Between series SD NULL | Intermediate precision SD NULL | Low limit of tolerance NULL | High limit of tolerance NULL |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0007245 | 0.0002245 | 0.0001373 | 1.0e-07 | 0.0002658 | 0.0002380 | 0.0012109 |
| 0.0015 | 0.0016887 | 0.0001887 | 0.0002630 | 0.0e+00 | 0.0003047 | 0.0012306 | 0.0021468 |
| 0.0200 | 0.0195872 | -0.0004128 | 0.0014254 | 6.0e-07 | 0.0016225 | 0.0171654 | 0.0220090 |
| 0.2000 | 0.1999305 | -0.0000695 | 0.0114413 | 7.6e-06 | 0.0117701 | 0.1830348 | 0.2168261 |
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0007245 | 44.8950192 | 144.89502 | 27.459237 | 53.167504 | -52.399408 | 142.189446 | FAIL |
| 0.0015 | 0.0016887 | 12.5798108 | 112.57981 | 17.534570 | 20.311394 | -17.958278 | 43.117900 | FAIL |
| 0.0200 | 0.0195872 | -2.0641339 | 97.93587 | 7.126778 | 8.112455 | -14.173073 | 10.044805 | FAIL |
| 0.2000 | 0.1999305 | -0.0347674 | 99.96523 | 5.720655 | 5.885032 | -8.482581 | 8.413046 | FAIL |
Accuracy profile are shown Figure 4.1. The đ˝-tolerance interval (blue lines) should be entirely within the acceptance limits (red dashed lines).
Figure 4.1: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile are shown Figure 4.2. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 4.2: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | 0.0000181 | -0.0019935 | 0.0020297 | 0.0009994 | 0.0181474 | 0.986 | |
| x | 0.9993616 | 0.9793459 | 1.0193772 | 0.0099437 | 100.5019077 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (FAIL)
| Test statistic | df | P value |
|---|---|---|
| 5.044 | 1 | 0.02471 * |
Trueness and precision are depicted on table 4.1 and 4.2
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias NULL | Repeatability SD NULL | Between series SD NULL | Intermediate precision SD NULL | Low limit of tolerance NULL | High limit of tolerance NULL |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003176 | -0.0001824 | 0.0001376 | 0.0e+00 | 0.0001376 | 0.0001219 | 0.0005133 |
| 0.0015 | 0.0012839 | -0.0002161 | 0.0002636 | 0.0e+00 | 0.0002636 | 0.0009091 | 0.0016587 |
| 0.0200 | 0.0192220 | -0.0007780 | 0.0014294 | 8.0e-07 | 0.0016996 | 0.0166384 | 0.0218056 |
| 0.2000 | 0.1999679 | -0.0000321 | 0.0114542 | 7.5e-06 | 0.0117785 | 0.1830626 | 0.2168732 |
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003176 | -36.4882817 | 63.51172 | 27.525333 | 27.525333 | -75.627610 | 2.651046 | FAIL |
| 0.0015 | 0.0012839 | -14.4058966 | 85.59410 | 17.570894 | 17.570894 | -39.390625 | 10.578832 | FAIL |
| 0.0200 | 0.0192220 | -3.8899630 | 96.11004 | 7.146753 | 8.497999 | -16.808075 | 9.028149 | FAIL |
| 0.2000 | 0.1999679 | -0.0160589 | 99.98394 | 5.727123 | 5.889253 | -8.468714 | 8.436596 | FAIL |
Accuracy profile are shown Figure 4.1. The đ˝-tolerance interval (blue lines) should be entirely within the acceptance limits (red dashed lines).
Figure 4.3: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile are shown Figure 4.2. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 4.4: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0003905 | -0.0024046 | 0.0016237 | 0.0010006 | -0.3902286 | 0.698 | |
| x | 1.0015911 | 0.9815504 | 1.0216318 | 0.0099561 | 100.6003838 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (FAIL)
| Test statistic | df | P value |
|---|---|---|
| 5.05 | 1 | 0.02462 * |
Trueness and precision are depicted on table 4.1 and 4.2
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias NULL | Repeatability SD NULL | Between series SD NULL | Intermediate precision SD NULL | Low limit of tolerance NULL | High limit of tolerance NULL |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003174 | -0.0001826 | 0.0001376 | 0.0e+00 | 0.0001376 | 0.0001218 | 0.0005130 |
| 0.0015 | 0.0012834 | -0.0002166 | 0.0002635 | 0.0e+00 | 0.0002635 | 0.0009088 | 0.0016580 |
| 0.0200 | 0.0192142 | -0.0007858 | 0.0014286 | 9.0e-07 | 0.0017009 | 0.0166273 | 0.0218012 |
| 0.2000 | 0.1998863 | -0.0001137 | 0.0114533 | 7.8e-06 | 0.0117893 | 0.1829597 | 0.2168130 |
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0003174 | -36.5154449 | 63.48456 | 27.511253 | 27.511253 | -75.634752 | 2.603862 | FAIL |
| 0.0015 | 0.0012834 | -14.4401297 | 85.55987 | 17.563399 | 17.563399 | -39.414202 | 10.533942 | FAIL |
| 0.0200 | 0.0192142 | -3.9288280 | 96.07117 | 7.142830 | 8.504340 | -16.863670 | 9.006014 | FAIL |
| 0.2000 | 0.1998863 | -0.0568324 | 99.94317 | 5.726666 | 5.894633 | -8.520142 | 8.406478 | FAIL |
Accuracy profile are shown Figure 4.1. The đ˝-tolerance interval (blue lines) should be entirely within the acceptance limits (red dashed lines).
Figure 4.5: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile are shown Figure 4.2. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 4.6: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0003903 | -0.0024057 | 0.0016251 | 0.0010013 | -0.3897947 | 0.698 | |
| x | 1.0011826 | 0.9811289 | 1.0212362 | 0.0099626 | 100.4942902 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (FAIL)
| Test statistic | df | P value |
|---|---|---|
| 5.025 | 1 | 0.02498 * |
Trueness and precision are depicted on table 4.1 and 4.2
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias NULL | Repeatability SD NULL | Between series SD NULL | Intermediate precision SD NULL | Low limit of tolerance NULL | High limit of tolerance NULL |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005245 | 0.0000245 | 0.0001382 | 0.0e+00 | 0.0001529 | 0.0002988 | 0.0007502 |
| 0.0015 | 0.0014933 | -0.0000067 | 0.0002644 | 0.0e+00 | 0.0002845 | 0.0010780 | 0.0019085 |
| 0.0200 | 0.0194800 | -0.0005200 | 0.0014350 | 7.0e-07 | 0.0016699 | 0.0169644 | 0.0219955 |
| 0.2000 | 0.2007199 | 0.0007199 | 0.0114500 | 6.2e-06 | 0.0117193 | 0.1839268 | 0.2175130 |
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005245 | 4.8951205 | 104.89512 | 27.633709 | 30.588690 | -40.246485 | 50.036726 | FAIL |
| 0.0015 | 0.0014933 | -0.4488081 | 99.55119 | 17.627064 | 18.967374 | -28.130321 | 27.232705 | FAIL |
| 0.0200 | 0.0194800 | -2.6001706 | 97.39983 | 7.174992 | 8.349560 | -15.177868 | 9.977527 | FAIL |
| 0.2000 | 0.2007199 | 0.3599375 | 100.35994 | 5.724989 | 5.859629 | -8.036602 | 8.756477 | FAIL |
Accuracy profile are shown Figure 4.1. The đ˝-tolerance interval (blue lines) should be entirely within the acceptance limits (red dashed lines).
Figure 4.7: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile are shown Figure 4.2. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 4.8: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0001857 | -0.0021921 | 0.0018206 | 0.0009967 | -0.1863452 | 0.853 | |
| x | 1.0043267 | 0.9843637 | 1.0242897 | 0.0099176 | 101.2676087 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (FAIL)
| Test statistic | df | P value |
|---|---|---|
| 5.346 | 1 | 0.02077 * |
Trueness and precision are depicted on table 4.1 and 4.2
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias NULL | Repeatability SD NULL | Between series SD NULL | Intermediate precision SD NULL | Low limit of tolerance NULL | High limit of tolerance NULL |
|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005101 | 0.0000101 | 0.0001380 | 0.0e+00 | 0.0001525 | 0.0002852 | 0.0007351 |
| 0.0015 | 0.0014779 | -0.0000221 | 0.0002641 | 0.0e+00 | 0.0002842 | 0.0010631 | 0.0018927 |
| 0.0200 | 0.0194454 | -0.0005546 | 0.0014333 | 7.0e-07 | 0.0016611 | 0.0169475 | 0.0219434 |
| 0.2000 | 0.2004922 | 0.0004922 | 0.0114412 | 5.9e-06 | 0.0116946 | 0.1837421 | 0.2172423 |
| Introduced concentrations NULL | Mean calculated concentrations NULL | Bias (%) | Recovery (%) | CV repeatability (%) | CV intermediate precision (%) | Low limit of tolerance (%) | High limit of tolerance (%) | Results |
|---|---|---|---|---|---|---|---|---|
| 0.0005 | 0.0005101 | 2.0241985 | 102.02420 | 27.599817 | 30.504080 | -42.96475 | 47.013147 | FAIL |
| 0.0015 | 0.0014779 | -1.4727244 | 98.52728 | 17.606452 | 18.948361 | -29.12827 | 26.182819 | FAIL |
| 0.0200 | 0.0194454 | -2.7727795 | 97.22722 | 7.166690 | 8.305595 | -15.26270 | 9.717137 | FAIL |
| 0.2000 | 0.2004922 | 0.2460936 | 100.24609 | 5.720583 | 5.847318 | -8.12897 | 8.621157 | FAIL |
Accuracy profile are shown Figure 4.1. The đ˝-tolerance interval (blue lines) should be entirely within the acceptance limits (red dashed lines).
Figure 4.9: Accuracy profiles (red dashed line: acceptance limits, blue lines: đ˝-tolerance intervals).
Linearity profile are shown Figure 4.2. You should check that the black line (linear model) should be superimposed on the red dashed identity line.
Figure 4.10: Linearity profiles (red dashed line: identity line, black lines: linear regression lines, blue lines: đ˝-tolerance intervals).
The p-value for the intercept is > 0.05 which is in favor of a non-significant value (PASS)
The p-value for the slope is < 0.05 which is in favor of a significant value (PASS)
| Estimate | CI (lower) | CI (upper) | Std. Error | t value | Pr(>|t|) | ||
|---|---|---|---|---|---|---|---|
| (Intercept) | -0.0001993 | -0.0022020 | 0.0018034 | 0.0009949 | -0.2003272 | 0.842 | |
| x | 1.0032564 | 0.9833293 | 1.0231835 | 0.0098997 | 101.3418223 | <0.001 | *** |
The p-value < 0.05 which is in favor of heterosedasticity and standard deviations of a calculated concentrations as related to introduced concentrations, are non-constant (FAIL)
| Test statistic | df | P value |
|---|---|---|
| 5.301 | 1 | 0.02131 * |
| ID | TYPE | SERIE | SIGNAL | CONC_LEVEL |
|---|---|---|---|---|
| CAL | CAL | 1 | 3057 | 0.0005 |
| CAL | CAL | 1 | 11600 | 0.0015 |
| CAL | CAL | 1 | 155620 | 0.0200 |
| CAL | CAL | 1 | 1556003 | 0.2000 |
| CAL | CAL | 1 | 1720 | 0.0005 |
| CAL | CAL | 1 | 7430 | 0.0015 |
| CAL | CAL | 1 | 145383 | 0.0200 |
| CAL | CAL | 1 | 1467917 | 0.2000 |
| CAL | CAL | 2 | 2144 | 0.0005 |
| CAL | CAL | 2 | 5250 | 0.0015 |
| CAL | CAL | 2 | 142242 | 0.0200 |
| CAL | CAL | 2 | 1425120 | 0.2000 |
| CAL | CAL | 2 | 1847 | 0.0005 |
| CAL | CAL | 2 | 8487 | 0.0015 |
| CAL | CAL | 2 | 137393 | 0.0200 |
| CAL | CAL | 2 | 1435514 | 0.2000 |
| CAL | CAL | 3 | 2744 | 0.0005 |
| CAL | CAL | 3 | 10473 | 0.0015 |
| CAL | CAL | 3 | 141074 | 0.0200 |
| CAL | CAL | 3 | 1400930 | 0.2000 |
| CAL | CAL | 3 | 3422 | 0.0005 |
| CAL | CAL | 3 | 10554 | 0.0015 |
| CAL | CAL | 3 | 115746 | 0.0200 |
| CAL | CAL | 3 | 1432539 | 0.2000 |
| ID | TYPE | SERIE | SIGNAL | CONC_LEVEL |
|---|---|---|---|---|
| VAL | VAL | 1 | 1544 | 0.0005 |
| VAL | VAL | 1 | 9992 | 0.0015 |
| VAL | VAL | 1 | 155683 | 0.0200 |
| VAL | VAL | 1 | 1767753 | 0.2000 |
| VAL | VAL | 1 | 1422 | 0.0005 |
| VAL | VAL | 1 | 11212 | 0.0015 |
| VAL | VAL | 1 | 154877 | 0.0200 |
| VAL | VAL | 1 | 1540288 | 0.2000 |
| VAL | VAL | 1 | 3661 | 0.0005 |
| VAL | VAL | 1 | 11527 | 0.0015 |
| VAL | VAL | 1 | 154062 | 0.0200 |
| VAL | VAL | 1 | 1466979 | 0.2000 |
| VAL | VAL | 1 | 2712 | 0.0005 |
| VAL | VAL | 1 | 6007 | 0.0015 |
| VAL | VAL | 1 | 153763 | 0.0200 |
| VAL | VAL | 1 | 1466715 | 0.2000 |
| VAL | VAL | 2 | 2593 | 0.0005 |
| VAL | VAL | 2 | 10558 | 0.0015 |
| VAL | VAL | 2 | 140350 | 0.0200 |
| VAL | VAL | 2 | 1413294 | 0.2000 |
| VAL | VAL | 2 | 2880 | 0.0005 |
| VAL | VAL | 2 | 9174 | 0.0015 |
| VAL | VAL | 2 | 110853 | 0.0200 |
| VAL | VAL | 2 | 1425878 | 0.2000 |
| VAL | VAL | 2 | 1316 | 0.0005 |
| VAL | VAL | 2 | 9065 | 0.0015 |
| VAL | VAL | 2 | 136750 | 0.0200 |
| VAL | VAL | 2 | 1368431 | 0.2000 |
| VAL | VAL | 2 | 1908 | 0.0005 |
| VAL | VAL | 2 | 9657 | 0.0015 |
| VAL | VAL | 2 | 130685 | 0.0200 |
| VAL | VAL | 2 | 1332873 | 0.2000 |
| VAL | VAL | 3 | 1498 | 0.0005 |
| VAL | VAL | 3 | 7730 | 0.0015 |
| VAL | VAL | 3 | 142770 | 0.0200 |
| VAL | VAL | 3 | 1430404 | 0.2000 |
| VAL | VAL | 3 | 3415 | 0.0005 |
| VAL | VAL | 3 | 10179 | 0.0015 |
| VAL | VAL | 3 | 141127 | 0.0200 |
| VAL | VAL | 3 | 1409384 | 0.2000 |
| VAL | VAL | 3 | 3423 | 0.0005 |
| VAL | VAL | 3 | 10600 | 0.0015 |
| VAL | VAL | 3 | 138551 | 0.0200 |
| VAL | VAL | 3 | 1403500 | 0.2000 |
| VAL | VAL | 3 | 1281 | 0.0005 |
| VAL | VAL | 3 | 6198 | 0.0015 |
| VAL | VAL | 3 | 117689 | 0.0200 |
| VAL | VAL | 3 | 1411380 | 0.2000 |
Aphalo, Pedro J. 2022a. Ggpmisc: Miscellaneous Extensions to Ggplot2. https://CRAN.R-project.org/package=ggpmisc.
Aphalo, Pedro J. 2022b. Ggpp: Grammar Extensions to Ggplot2. https://CRAN.R-project.org/package=ggpp.
Dahl, David B., David Scott, Charles Roosen, Arni Magnusson, and Jonathan Swinton. 2019. Xtable: Export Tables to LaTeX or HTML. http://xtable.r-forge.r-project.org/.
DarĂłczi, Gergely, and Roman Tsegelskyi. 2022. Pander: An r Pandoc Writer. https://rapporter.github.io/pander/.
Dowle, Matt, and Arun Srinivasan. 2022. Data.table: Extension of âData.frameâ. https://CRAN.R-project.org/package=data.table.
Fox, John, and Sanford Weisberg. 2019. An R Companion to Applied Regression. Third. Thousand Oaks CA: Sage. https://socialsciences.mcmaster.ca/jfox/Books/Companion/.
Fox, John, Sanford Weisberg, and Brad Price. 2022a. Car: Companion to Applied Regression. https://CRAN.R-project.org/package=car.
Fox, John, Sanford Weisberg, and Brad Price. 2022b. carData: Companion to Applied Regression Data Sets. https://CRAN.R-project.org/package=carData.
Garnier, Simon. 2021. Viridis: Colorblind-Friendly Color Maps for r. https://CRAN.R-project.org/package=viridis.
Garnier, Simon.. 2022. viridisLite: Colorblind-Friendly Color Maps (Lite Version). https://CRAN.R-project.org/package=viridisLite.
Hofner, Benjamin. 2021. papeR: A Toolbox for Writing Pretty Papers and Reports. https://CRAN.R-project.org/package=papeR.
Hofner, Benjamin, and with contributions by many others. 2021. papeR: A Toolbox for Writing Pretty Papers and Reports. https://github.com/hofnerb/papeR.
Hothorn, Torsten, Achim Zeileis, Richard W. Farebrother, and Clint Cummins. 2022. Lmtest: Testing Linear Regression Models. https://CRAN.R-project.org/package=lmtest.
R Core Team. 2022. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Sievert, Carson. 2020. Interactive Web-Based Data Visualization with r, Plotly, and Shiny. Chapman; Hall/CRC. https://plotly-r.com.
Sievert, Carson, Chris Parmer, Toby Hocking, Scott Chamberlain, Karthik Ram, Marianne Corvellec, and Pedro Despouy. 2022. Plotly: Create Interactive Web Graphics via Plotly.js. https://CRAN.R-project.org/package=plotly.
Wickham, Hadley. 2016. Ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org.
Wickham, Hadley, and Jennifer Bryan. 2022. Readxl: Read Excel Files. https://CRAN.R-project.org/package=readxl.
Wickham, Hadley, Winston Chang, Lionel Henry, Thomas Lin Pedersen, Kohske Takahashi, Claus Wilke, Kara Woo, Hiroaki Yutani, and Dewey Dunnington. 2022. Ggplot2: Create Elegant Data Visualisations Using the Grammar of Graphics. https://CRAN.R-project.org/package=ggplot2.
Wickham, Hadley, Romain François, Lionel Henry, and Kirill Mßller. 2022. Dplyr: A Grammar of Data Manipulation. https://CRAN.R-project.org/package=dplyr.
Zeileis, Achim, and Gabor Grothendieck. 2005. âZoo: S3 Infrastructure for Regular and Irregular Time Series.â Journal of Statistical Software 14 (6): 1â27. https://doi.org/10.18637/jss.v014.i06.
Zeileis, Achim, Gabor Grothendieck, and Jeffrey A. Ryan. 2022. Zoo: S3 Infrastructure for Regular and Irregular Time Series (zâs Ordered Observations). https://zoo.R-Forge.R-project.org/.
Zeileis, Achim, and Torsten Hothorn. 2002. âDiagnostic Checking in Regression Relationships.â R News 2 (3): 7â10. https://CRAN.R-project.org/doc/Rnews/.
Zhu, Hao. 2021. kableExtra: Construct Complex Table with Kable and Pipe Syntax. https://CRAN.R-project.org/package=kableExtra.